I know of an INTP who was attracted to very complicated scenarios. He loved to get dropped into a difficult mental puzzle (love triangle) in order to work his way out of it. I think it was more the hours of silent thought provocation, and less the competition element, which attracted him to it. I have no patience for that sort of thing due to the human element, but I enjoy different types of non-human puzzles immensely.

It seems to me to be more of an introverted type of pasttime, but I could be mistaken. It just seems like something someone would do if s/he wanted to spend hours inside his or her own head. But who knows.

I have nothing with love triangles. Or well, I may actually despise them. At least fictional ones. They sure annoy the crap out of me on TV, in shows and movies. They're always portrayed way too shallow though, and I've never seen love triangle stuff in a show on TV that was not really badly written.